Abstract
This paper concerns a class of group-lasso learning problems where the objective function is the sum of an empirical loss and the group-lasso penalty. For a class of loss function satisfying a quadratic majorization condition, we derive a unified algorithm called groupwise-majorization-descent (GMD) for efficiently computing the solution paths of the corresponding group-lasso penalized learning problem. GMD allows for general design matrices, without requiring the predictors to be group-wise orthonormal. As illustration examples, we develop concrete algorithms for solving the group-lasso penalized least squares and several group-lasso penalized large margin classifiers. These group-lasso models have been implemented in an R package gglasso publicly available from the Comprehensive R Archive Network (CRAN) at http://cran.r-project.org/web/packages/gglasso. On simulated and real data, gglasso consistently outperforms the existing software for computing the group-lasso that implements either the classical groupwise descent algorithm or Nesterov’s method.
Original language | English (US) |
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Pages (from-to) | 1129-1141 |
Number of pages | 13 |
Journal | Statistics and Computing |
Volume | 25 |
Issue number | 6 |
DOIs | |
State | Published - Nov 30 2015 |
Bibliographical note
Funding Information:The authors thank the editor, an associate editor and two referees for their helpful comments and suggestions. This work is supported in part by NSF Grant DMS-08-46068.
Publisher Copyright:
© 2014, Springer Science+Business Media New York.
Keywords
- Group lasso
- Groupwise descent
- Large margin classifiers
- MM principle
- SLEP
- grplasso